The Red Devils look set to miss out on the top four unless an unlikely series of results occur.
Manchester United are sixth behind Chelsea and Arsenal and are a mammoth 27 points behind Premier League leaders Manchester City.
Ole Gunnar Solskjaer’s side are facing the prospect of playing Europa League football next season as a result.
And Herrera, who has yet to sign a new contract at Old Trafford, believes all of the players have to take responsibility.
“I don’t like to talk personally, I like to talk as a group,” Herrera told the club’s website.
“I think football is a team sport.
“I think you have to analyse the season from the team point of view and we are disappointed.
“To be honest, when a manager is sacked, for me it’s also the responsibility of the players. We have to take responsibility for it – it is not only the manager and the staff.
“The players have a big responsibility and that’s why I think we should all feel disappointed because we haven’t been able to achieve the objectives.
“For me, the objectives for this club for every season should be fighting for the titles and we haven’t fought for them so let’s take responsibility, every player.”
Herrera has also spoken on finding it tough watching from the sidelines as he has struggled with injury.
He explained: “I love playing and being part of the group. Even in the bad moments, I like to be involved, to put my effort and my work and my commitment in for my team-mates, for the club, for the team.
“I haven’t been able to play and I’m a very bad patient when I’m injured – my family can tell you that!
“Now I’m back, the other day I felt good, I’ve felt good since my last injury.
“I’m feeling good and I will just try to give my best in the last two games of the season.
“I really suffer when I’m not involved. I’m not talking about playing or not playing, I just want to be available, I just want to be an option for the manager and I haven’t been an option for the last three or four weeks when we have had some important fixtures.
“I’m a really bad patient – if you speak to my family, they will tell you that. But I don’t want to think about this now.
“I want to think about what is coming in the next two games – try to get the six points and after let’s see if Chelsea make some mistakes.”
United return to action on Sunday when they travel to Huddersfield (2pm).